Have a personal or library account? Click to login
Fermat’s Little Theorem via Divisibility of Newton’s Binomial Cover

Fermat’s Little Theorem via Divisibility of Newton’s Binomial

Formalized Mathematics
Volume 23 (2015): Issue 3 (September 2015)
By: Rafał Ziobro  
Open Access
|Sep 2015

References

  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  4. [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
    Search in Google Scholar
  5. [5] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
    Search in Google Scholar
  6. [6] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
    Search in Google Scholar
  7. [7] Czesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
    Search in Google Scholar
  8. [8] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
    Search in Google Scholar
  9. [9] Marco B. Caminati and Giuseppe Rosolini. Custom automations in Mizar. Journal of Automated Reasoning, 50(2):147-160, 2013.10.1007/s10817-012-9266-1
    Search in Google Scholar
  10. [10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
    Search in Google Scholar
  11. [11] Yoshinori Fujisawa and Yasushi Fuwa. The Euler’s function. Formalized Mathematics, 6 (4):549-551, 1997.
    Search in Google Scholar
  12. [12] Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Euler’s Theorem and small Fermat’s Theorem. Formalized Mathematics, 7(1):123-126, 1998.
    Search in Google Scholar
  13. [13] Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Public-key cryptography and Pepin’s test for the primality of Fermat numbers. Formalized Mathematics, 7(2):317-321, 1998.
    Search in Google Scholar
  14. [14] Jacek Gancarzewicz. Arytmetyka, 2000. In Polish.
    Search in Google Scholar
  15. [15] Krzysztof Hryniewiecki. Recursive definitions. Formalized Mathematics, 1(2):321-328, 1990.
    Search in Google Scholar
  16. [16] Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4): 573-577, 1997.
    Search in Google Scholar
  17. [17] Artur Korniłowicz. On rewriting rules in Mizar. Journal of Automated Reasoning, 50(2): 203-210, 2013.10.1007/s10817-012-9261-6
    Search in Google Scholar
  18. [18] Artur Korniłowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179-186, 2004.
    Search in Google Scholar
  19. [19] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.
    Search in Google Scholar
  20. [20] Richard Krueger, Piotr Rudnicki, and Paul Shelley. Asymptotic notation. Part II: Examples and problems. Formalized Mathematics, 9(1):143-154, 2001.
    Search in Google Scholar
  21. [21] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
    Search in Google Scholar
  22. [22] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829-832, 1990.
    Search in Google Scholar
  23. [23] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
    Search in Google Scholar
  24. [24] Konrad Raczkowski. Integer and rational exponents. Formalized Mathematics, 2(1):125-130, 1991.
    Search in Google Scholar
  25. [25] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.
    Search in Google Scholar
  26. [26] Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.
    Search in Google Scholar
  27. [27] Christoph Schwarzweller. Modular integer arithmetic. Formalized Mathematics, 16(3): 247-252, 2008. doi:10.2478/v10037-008-0029-8.10.2478/v10037-008-0029-8
    Search in Google Scholar
  28. [28] Wacław Sierpinski. Teoria liczb. 1950. In Polish.
    Search in Google Scholar
  29. [29] Wacław Sierpinski. O rozwiazywaniu rownan w liczbach całkowitych, 1956. In Polish.
    Search in Google Scholar
  30. [30] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
    Search in Google Scholar
  31. [31] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.
    Search in Google Scholar
  32. [32] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
    Search in Google Scholar
  33. [33] Li Yan, Xiquan Liang, and Junjie Zhao. Gauss lemma and law of quadratic reciprocity. Formalized Mathematics, 16(1):23-28, 2008. doi:10.2478/v10037-008-0004-4.10.2478/v10037-008-0004-4
    Search in Google Scholar
  34. [34] Rafał Ziobro. Some remarkable identities involving numbers. Formalized Mathematics, 22(3):205-208, 2014. doi:10.2478/forma-2014-0023. 10.2478/forma-2014-0023
    Search in Google Scholar
DOI: https://doi.org/10.1515/forma-2015-0018 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Journal RSS Feed
Language: English
Page range: 215 - 229
Submitted on: Jun 30, 2015
|
Published on: Sep 30, 2015
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
factorization,
primes,
Fermat
Related subjects:
Mathematics,
General mathematics,
Computer sciences,
Computer sciences, other

© 2015 Rafał Ziobro, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Previous articleVolume 23 (2015): Issue 3 (September 2015)Next article